Richard von Mises Lecture 2026

Abstracts

From Simulation to Decision Intelligence: A Mathematical Roadmap for Scientific Machine Learning

Wil Schilders (TU Eindhoven · Hans Fischer senior fellow at TUM-IAS · ICIAM president)

Over the past decades, computational science has reached a remarkable level of maturity: in principle, we are able to simulate highly complex systems with great accuracy. Yet in practice, simulation remains underused where it matters most — namely in fast, real-world decision-making processes. This paradox reflects a fundamental gap between capability and usability: models are often too slow, too complex, and insufficiently robust to be integrated into modern workflows.

Scientific machine learning offers a promising route forward by combining data-driven approaches with classical modelling. However, current methods frequently lack the reliability, interpretability, and guarantees required for deployment in industrial and scientific settings. In this lecture, we argue that bridging this gap requires a shift from black-box learning to structure-aware modelling, in which mathematical principles, such as stability, model reduction, and the enforcement of physical laws, are embedded by design.

This perspective leads to an ambitious vision: simulation as a real-time, adaptive, and trustworthy component of decision-making, forming the backbone of emerging concepts such as digital twins. Realizing this vision will require mathematics not only to support, but to guide and shape the development of scientific machine learning, continuing the tradition of Richard von Mises, who viewed mathematics as an integral part of the scientific enterprise.

Stochastic Optimal Control with Partial Future Information

Huilin Zhang (HU Berlin)

Stochastic control theory studies how to make optimal decisions in systems that evolve randomly over time. It has deep connections with probability theory, differential equations, economics, finance, engineering, and data science. Classical stochastic control problems assume that decisions can only depend on present and past information, reflecting the natural principle that the future is unknown. However, many realistic situations challenge this assumption. In financial markets, for instance, traders may possess partial insider information about future events; in modern data-driven applications, predictive signals extracted from historical data may provide probabilistic insight into future behavior. Such settings motivate the study of stochastic control problems with future information, where the controller is allowed to use anticipative information when making decisions.

This talk introduces recent progress in the mathematical analysis of stochastic optimal control under this anticipative framework. The presence of future information fundamentally changes the structure of the problem and places it outside the reach of classical stochastic control theory. In particular, many standard tools rely heavily on the assumption that controls are non-anticipative, meaning they depend only on currently available information. Once this assumption is relaxed, new mathematical difficulties arise in both the formulation and analysis of the control problem.

To overcome these challenges, we employ ideas from the recently developed theory of rough stochastic analysis. Rough path theory, originally introduced to extend calculus beyond classical smooth settings, provides a robust framework for handling highly irregular signals. Within this new-developed rough stochastic framework, we establish two central principles of optimal control theory: the dynamic programming principle and Pontryagin’s maximum principle. The dynamic programming principle describes how global optimization problems can be decomposed into smaller local problems, while Pontryagin’s maximum principle characterizes optimal controls through variational arguments and associated adjoint equations. Together, these results provide a rigorous foundation for studying stochastic control problems involving future information.

References

1. F. Bugini, P. K. Friz, K. Lê, H.-L. Z. Rough stochastic filtering. ArXiv:2509.11825. 2026.
2. P. K. Friz, K. Le, and H.-L. Z. Controlled rough SDEs, pathwise stochastic control and dynamic programming principles, ArXiv:2412.05698, 2024.
3. U. Horst and H.-L. Z. Pontryagin Maximum Principle for rough stochastic systems and pathwise stochastic control. ArXiv:2503.22959, 2025.